Answer Happy

K S Question 2. (25 pts.) Consider the normal form game from THE-1 Question 4 that involves a shoot-out for a prize of K amounts of consumption good (where K stands for kapital). There are N > 2 players, each of whom has a gun with only one bullet. Each of the players decides whom to shoot if they choose to do so. (The shot agent leaves the game with certainty.) A player has the option to shoot any one of the other players, himself, and nobody at all. An agent wants to survive but gets more utility when the number of survivors gets smaller. This is captured by the following model for preferences. Each player gets a utility of zero if that player is shot by somebody (including himself). Meanwhile, if he is one of the s < N survivors, then he gets a utility of a. (7.5 pts.) Can there be a Nash equilibrium (an action profile passing the best response test) such that none of the players shoot any other player? If so, show it. If not, identify the deviator and her strictly profitable deviation opportunity. b. (7.5 pts.) Can there be a Nash equilibrium (an action profile passing the best response test) in which a player shoots himself? If so, show it. If not, identify the deviator and her strictly profitable deviation opportunity. c. (10 pts.) Identify the pure strategy best responses of any of the players i e N under A.0 and A.1. N